Tangential Velocity and the Moon

I've been doing a bit of independent study on Gravitation. What I find confusing is why the moon doesn't fall straight into the earth. I know that the moon has tangential velocity, but what exactly is tangential velocity? How does it apply to the moon not falling into the earth?

One way to envision orbits is via Newton's cannon. Imagine a very tall mountain, one so tall it rises out of the atmosphere. Now imagine a very powerful cannon atop this mountain. The muzzle velocity of the cannonball depends on the amount of shot put into the cannon.

Put just a little shot in the cannon and the cannonball will fall to Earth along what appears to be a parabolic trajectory. Add a bit more shot and the cannonball will still fall to Earth, but with ever more shot it becomes obvious that this parabolic trajectory is but an approximation. A better model is a segment of an ellipse.

The cannonball hits the Earth further and further from the mountain as the muzzle velocity increases. With just the right muzzle velocity, the cannonball will hit the Earth at a point diametrically opposed to the mountain. Now what happens if you add just a bit more shot to the cannon? The answer is that the cannonball will go all the way around the Earth. If the cannon is moved out of the way in the ~90 minutes it takes for the cannonball to go around the Earth, it will keep following this path forever. The cannonball is in orbit about the Earth.

One way to envision orbits is via Newton's cannon. Imagine a very tall mountain, one so tall it rises out of the atmosphere. Now imagine a very powerful cannon atop this mountain. The muzzle velocity of the cannonball depends on the amount of shot put into the cannon.

Put just a little shot in the cannon and the cannonball will fall to Earth along what appears to be a parabolic trajectory. Add a bit more shot and the cannonball will still fall to Earth, but with ever more shot it becomes obvious that this parabolic trajectory is but an approximation. A better model is a segment of an ellipse.

The cannonball hits the Earth further and further from the mountain as the muzzle velocity increases. With just the right muzzle velocity, the cannonball will hit the Earth at a point diametrically opposed to the mountain. Now what happens if you add just a bit more shot to the cannon? The answer is that the cannonball will go all the way around the Earth. If the cannon is moved out of the way in the ~90 minutes it takes for the cannonball to go around the Earth, it will keep following this path forever. The cannonball is in orbit about the Earth.

So, hypothetically, if the cannonball needs to be shot at 1000 m/s to start orbiting the Earth then 1000 m/s is the tangential velocity?

Imagine standing on a cliff, say 10 feet back from the edge, and throwing a rock over the edge. From the time the rock leaves your hand, the only force acting on the rock is gravity which acts straight down. But the rock does not go straight down- the downwar force causes an acceleration downward which then causes motion downward. But all this time the rock is moving forward due to the forward velocity you gave. The rock does go downward, of course, but not until after it has "missed" the edge of the cliff.

The same thing happens with the moon (or any satellite)- it is pulled downward but with the additional forward motion, the moon just keeps "missing" the earth.